Abstract. The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulence is alternatively represented by: 1) an explicit, observation–based, scale–dependent eddy diffusivity, 2) stochastic noise, added to a deterministic velocity field, or 3) explicit and implicit diffusion in a spectral numerical model of Navier–Stokes equations. Lagrangian chaos in our model occurs only within distinct regions of the eddy, including a large chaotic ‘sea’ that fills much of the volume near the perimeter and central axis of the eddy, and much smaller ‘resonant’ bands. The size and distribution of these regions depends on factors such as the degree of axial asymmetry of the eddy and the Ekman number. The relative importance of chaotic advection and turbulent diffusion within the chaotic regions is quantified using three measures: the ratio of the tracer filament arrest scale to the width of the chaotic region, the rate of dispersal of closely spaced fluid parcels, and the Nakamura effective diffusivity. The role of chaotic advection in the stirring of a passive tracer is generally found to be most important within the larger chaotic ‘seas’, at intermediate times, with small diffusivities, and for eddies with strong asymmetry. In contrast, in thin chaotic regions, turbulent diffusion at oceanographically relevant rates is at least as important as chaotic advection. Future work should address anisotropic and spatially–varying representations of turbulence for more realistic models.
Competition between Chaotic Advection and Diffusion: Stirring and Mixing in a 3D Eddy Model